Magnoelastic coupling in magnetic oxide nanoparticles

Phonons are exquisitely sensitive to finite length scale effects in a wide variety of materials. To investigate confinement in combination with strong magnetoelastic interactions, we measured the infrared vibrational properties of MnO and CoFe$_2$O$_4$ nanoparticles and their parent compounds. For MnO, a charge and bonding analysis reveals that Born effective charge, local effective charge, total polarizability, and the force constant are overall lower in the nanoparticles compared to the bulk. We find that the spin-lattice coupling drops from $\sim$7 cm$^{-1}$ in the single crystal to $<$1 cm$^{-1}$ in the nanoparticles. For CoFe$_2$O$_4$, the spectroscopic response is sensitive to the size-induced crossover to the superparamagnetic state, which occurs between 7 and 10 nm, and a spin-phonon coupling analysis supports the core-shell model. Moreover, it provides an estimate of the thickness of the magnetically disordered shell, increasing from 0.4 nm in the 14 nm particles to 0.8 nm in the 5 nm particles, demonstrating that the associated local lattice distortions take place on the length scale of the unit cell. These findings are important for understanding finite length scale effects in magnetic oxides and other more complex functional oxides.